On the Indicator of Growth of Entire Functions of Exponential Type in Infinite Dimensional Spaces and the Levi Problem in Infinite Dimensional Projective Spaces

Masaru Nishihara

Abstract: Let $E$ be a separable complex Fréchet space with the bounded approximation property, or a complex DFN-space and $\bfc{P}(E)$ be the complex projective space induced from $E$. Then we solve affirmatively the Levi problem in a Riemann domain over the projective space $\bfc{P}(E)$. By using this result, we give the infinite dimensional version of the indicator theorem of entire functions of exponential type on $\bfc{C}^{n}$.

Full text of the article:

• Compressed PostScript file (148 kilobytes)
• PDF file (300 kilobytes)